On the accuracy of the algebraic approximation in molecular electronic structure calculations: VI. Matrix Hartree - Fock and many-body perturbation theory calculations for the ground state of the water molecule

Abstract

The use of distributed Gaussian basis sets in reducing the total basis set truncation error in matrix Hartree - Fock and second-order many-body perturbation theory calculations is investigated for the ground state of the water molecule at its equilibrium geometry. A distributed basis set of even-tempered Gaussian functions centred not only on the atomic nuclei but also on the O - H bond centres and at the midpoint of the line H - H is shown to give a matrix Hartree - Fock energy of . For diatomic molecules, distributed basis sets of this type have been shown to yield matrix Hartree - Fock energies which approach an accuracy of . The present distributed basis set, which includes functions of s, p, d and f symmetry, is employed in a second-order many-body perturbation theory study of correlation effects recovering 97.6% of an estimate of the exact second-order correlation energy given by Klopper. The effects of higher harmonics in the basis set are investigated and a basis set, which includes functions of s, p, d, f and g symmetry, is shown to be capable of recovering 98.6% of the exact second-order energy. The reliability of simple extrapolation techniques to estimate the effects of basis functions of h symmetry and higher is investigated and shown to support 99.8% of the estimate of the exact second-order correlation energy component.